container # | weight |
container 1 | 15 |
container 2 | 10 |
container 3 | 45 |
container 4 | 37 |
container 5 | 20 |
container 6 | 31 |
container 7 | 35 |
container 8 | 40 |
container 9 | 19 |
container 10 | 22 |
mean value = | 15+10+45+37+20+31+35+40+19+22 ----------------------------------------------- 10 |
= 23 kg |
mean value μ = | a_{1} + a_{2} + ...+ a_{N} -------------------------- N |
= | 1 --- N |
Σ a_{i} (equation 1) |
mean value = | 14+22+14+17+18+24+22+22+23+18+16 -------------------------------------------------------- 10 |
= | 160 ---- 10 |
=16 |
σ = | √ | ( | 1 --- N |
Σ (a_{i} - μ)^{2} | ) | = | 4.8 |
= | 1 --- N |
Σ |a_{i} -μ| (not the generally accepted equation) |
σ = | √ | ( | 1 --- N |
Σ (a_{i} - μ)^{2} | ) (equation 2) |
σ = | √ | ( | 1 --- N |
Σ (a_{i} - μ)^{2} | ) (equation 2) |
var = | 1 --- N |
Σ (a_{i} - μ)^{2} (equation 3) |
mean value μ = | a_{1} + a_{2} + ...+ a_{N} -------------------------- N |
= | 1 --- N |
Σ a_{i} (equation 1) |
σ = | √ | ( | 1 --- N |
Σ (a_{i} - μ)^{2} | ) (equation 2) |
x̄ = | 1 -- n |
Σ b_{i} (equation 3) |
s = | √ | ( | 1 --- n-1 |
Σ (b_{i} - x̄)^{2} | ) (equation 4) |
s = | √ | ( | 1 - n |
Σ (b_{i} - x̄)^{2} | ) (equation 4") |
μ = | Σ f_{i} m_{i} -------- (equation 5) Σ f_{i} |
μ = | Σ f_{i} m_{i} ------- (equation 6) N |
σ = | √ | ( | 1 --- N |
Σ f_{i} (m_{i} - μ)^{2} | ) (equation 7) |
Class: | Freq. or counts: |
10-14 | 3 |
15-19 | 8 |
20-24 | 6 |
25-29 | 1 |
Class: | Freq. or counts: | Midpoint: | Midpoint x Freq. |
10-14 | 3 | 12 | 36 |
15-19 | 8 | 17 | 136 |
20-24 | 6 | 22 | 132 |
25-29 | 1 | 27 | 27 |
μ = | Σ f_{i} m_{i} -------- Σ f_{i} |
= | 331 ---- 18 |
= 18.4 |
number of combinations = |
n! ------- k!(n-k)! |
= |
3! ------- 2!(3-2)! |
= |
6 -- = 3 2 |
number of combinations of k out of n = |
┌ n ┐ └ k ┘ |
= |
n! ------- (equation 11) k!(n-k)! |
n! ------- k!(n-k)! |
┌ n ┐ └ k ┘ |
number of permutations of k out of n | = |
n! ----- (equation 12) (n-k)! |
3! ----- (3-2)! |
= |
3 x 2 x 1 ---------- 1 |
= 6 |
P(outcome=3) = | 1 -- 6 |
P(f) = | N_{f} -- (equation 13) N_{T} |
P(ace) = | 4 -- 52 |
P(k) = |
┌ n ┐ └ k ┘ |
p^{k} (1-p)^{n-k} (equation 18) |
P(X=2) = |
┌ 3 ┐ └ 2 ┘ |
0.4^{2} 0.6^{1} | = (about) 0.29 |
P(A|B) = | P(A ⋂ B) ---------- P(B) |
x̄ | = | 1 -- n |
Σ b_{i} | = | 10.8 |
p̂ | = | 62 -- 1000 |
= | 0.62 |
p̂ | = | 120 --- 500 |
= | 0.24 |
σ | = | √ ( | p̂ (1-p̂) ------ n |
) |
σ | = | √ ( | 0.24 (1 - 0.24;) -------------- 500 |
) | = 0.019 |
[ | x̄ -2 | S ---- √n |
; | x̄ +2 | S ---- √n |
] |